Global structure of an elliptic fibration
Global structure of an elliptic fibration
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椭圆纤维化的整体结构
DOI：
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发表时间：
2002
期刊：
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通讯作者：
N. Nakayama
中科院分区：
文献类型：
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作者：
N. Nakayama
本文在有边界的解析空间中引入了拟格拓扑，作为拟格拓扑的一个类比.本文将局部投射椭圆纤维化作为相应基本椭圆纤维化的拓扑中的扭子来研究。相关的椭圆上同调群对椭圆纤维化的结构有着丰富的信息。特别是，上野的扩展问题的答案，关系到Tate-Shafarevich群和它们的有限性，射影和Kahler椭圆纤维化的特征，和推广的对数变换到任意维数。本文是[N5]的修订版。
∂-etale topology is introduced for analytic spaces with boundary as an analog of etale topology for schemes. A locally projective elliptic fibration is bimeromorphically considered as a torsor in the ∂-etale topology of the associated basic elliptic fibration. The related ∂-etale cohomology groups have much information on the structure of elliptic fibrations. In particular, an answer to Ueno's extension problem, a relation to Tate-Shafarevich groups and their finiteness properties, characterizations of projective and Kahler elliptic fibrations, and a generalization of logarithmic transformation to arbitrary dimension are obtained. This article is a revised version of [N5].